Smooth shading is seemingly creating incorrect normals
Sometimes this happens for no apparent reasons. I have gotten into the same issue several times when importing models from other 3d packages. The only way to quickly remove them if apply normals and smooth shading doesn't work, is to ....


Delete the faces only, around the affected vertice and the edges undeleted.
Hit X to delete and choose "face only".
Turn on F2 add-on in the user preferences.
Select adjacent edges and hit F, to fill it with a face between them.


You should now how a clean mesh with the correct normals.


  Note Only use this method if Ctrl + N and applying smooth shading on the model does not solve the problem


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